-7x(x+4)=-43+8x

Solution for -7x(x+4)=-43+8x equation:

Simplifying
-7x(x + 4) = -43 + 8x

Reorder the terms:
-7x(4 + x) = -43 + 8x
(4 * -7x + x * -7x) = -43 + 8x
(-28x + -7x2) = -43 + 8x

Solving
-28x + -7x2 = -43 + 8x

Solving for variable 'x'.

Reorder the terms:
43 + -28x + -8x + -7x2 = -43 + 8x + 43 + -8x

Combine like terms: -28x + -8x = -36x
43 + -36x + -7x2 = -43 + 8x + 43 + -8x

Reorder the terms:
43 + -36x + -7x2 = -43 + 43 + 8x + -8x

Combine like terms: -43 + 43 = 0
43 + -36x + -7x2 = 0 + 8x + -8x
43 + -36x + -7x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
43 + -36x + -7x2 = 0

Factor a trinomial.
(1 + -1x)(43 + 7x) = 0

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(43 + 7x)' equal to zero and attempt to solve:

Simplifying
43 + 7x = 0

Solving
43 + 7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-43' to each side of the equation.
43 + -43 + 7x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 7x = 0 + -43
7x = 0 + -43

Combine like terms: 0 + -43 = -43
7x = -43

Divide each side by '7'.
x = -6.142857143

Simplifying
x = -6.142857143
Solution
x = {1, -6.142857143}